Summary: Domain Theory and the Logic of Observable
Properties
Samson Abramsky
Submitted for the degree of Doctor of Philosophy
Queen Mary College
University of London
October 31st 1987
Abstract
The mathematical framework of Stone duality is used to synthesize a number
of hitherto separate developments in Theoretical Computer Science:
· Domain Theory, the mathematical theory of computation introduced
by Scott as a foundation for denotational semantics.
· The theory of concurrency and systems behaviour developed by Milner,
Hennessy et al. based on operational semantics.
· Logics of programs.
Stone duality provides a junction between semantics (spaces of points =
denotations of computational processes) and logics (lattices of properties of
processes). Moreover, the underlying logic is geometric, which can be com-
putationally interpreted as the logic of observable properties--i.e. properties
which can be determined to hold of a process on the basis of a finite amount